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        <h1><span style="font-size:22px">Siggraph 2019</span></h1>
        <h1><span style="font-size:36px">MeshCNN: A Network with an Edge</span></h1>
        <div class="authors">
            <span style="font-size:18px"><a href="https://www.cs.tau.ac.il/~hanocka/" target="new">Rana Hanocka<sup>1</sup></a></span>
            &nbsp;
            <span style="font-size:18px"><a href="http://pxcm.org/" target="new">Amir Hertz<sup>1</sup></a></span>
            &nbsp;
            <span style="font-size:18px"><a href="https://www.cs.tau.ac.il/~noafish/" target="new">Noa Fish<sup>1</sup></a></span>
            &nbsp;
            <span style="font-size:18px"><a href="http://web.eng.tau.ac.il/~raja/" target="new">Raja Giryes<sup>1</sup></a></span>
            &nbsp;
            <span style="font-size:18px"><a href="https://scholar.google.co.il/citations?user=nEpKS-8AAAAJ&hl=en" target="new">Shachar Fleishman<sup>2</sup></a></span>
            &nbsp;
            <span style="font-size:18px"><a href="https://www.cs.tau.ac.il/~dcor/" target="new">Daniel Cohen-Or<sup>1</sup></a></span>
            <br>
            <span style="font-size:18px"><sup>1</sup>Tel Aviv University &nbsp;&nbsp;&nbsp; <sup>2</sup>Amazon<br><br></span>
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              <a href="https://bit.ly/meshcnn" target="_blank">
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              <h3 class="mb-3">Paper</h3>
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              <h3 class="mb-3">Bibtex</h3>
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    <h2>Abstract</h2>
Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology,
    and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity
    and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling
    operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN,
    a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines
    specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic
    connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied
    via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the
    subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network
    exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness
    of our task-driven pooling on various learning tasks applied to 3D meshes.
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    <h2>Video</h2>
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    <h2>The Layers of MeshCNN</h2>
    In MeshCNN the edges of a mesh are analogous to pixels in an image, since they are the basic building blocks
    for all CNN operations. Just as images start with a basic input feature: an RGB value per pixel;
    MeshCNN starts with a few basic geometric features per edge. The input edge feature is a 5-dimensional vector
    every edge: the dihedral angle, two inner angles and two edge-length ratios for each face.
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            <img src="imgs/input_edge_features.png" height="150px">
            <h4>Input Edge Features</h4>
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    MeshCNN learns features on the edges of the mesh, since every edge is incident to exactly two faces (triangles),
    which defines a natural fixed-sized convolutional neighborhood of four edges.
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            <img src="imgs/mesh_conv.png" height="150px">
            <h4>Mesh Convolution</h4>
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    Learned convolutional filters are applied on each edge feature vector and the 4 one-ring neighbors.
    The consistent face normal order is used to apply a symmetric convolution operation, which learns edge
    features that are invariant to rotations, translations and uniform scale.
    Mesh pooling downsamples the number of features in the network, by performing a edge-collapse on the learned
    edge features. The new edge neighbors are computed dynamically inside the network, and used in the next convolutions.
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            <img src="imgs/mesh_pool_unpool.png" height="150px">
            <h4>Mesh Pooling & Unpooling </h4>
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    For fully-convolutional tasks (such as segmentation), a mesh unpooling operation is used to restore the
    original mesh resolution.
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    <h2>Results</h2>
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            <img src="imgs/cubes.png" width="600px">
            <img src="imgs/cubes2.png" width="600px">
            <h4>Learned Simplifications on Cube Dataset </h4>
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            <img src="imgs/T76.png" width="550px"> <br>
            <img src="imgs/T18.png" width="550px">
            <h4>Learned Simplifications on Shrec Dataset </h4>
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            <img src="imgs/shrec__10_0.png" height="160px">
            <img src="imgs/shrec__14_0.png" height="160px">
            <img src="imgs/shrec__2_0.png" height="160px">
            <h4>Human Segmentation Results </h4>
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            <img src="imgs/coseg_alien.png" width="550px"> <br>
            <img src="imgs/coseg_chair.png" width="550px"> <br>
            <img src="imgs/coseg_vase.png" width="550px">
            <h4>Coseg Segmentation Results </h4>
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    <h2>Download Datasets</h2>
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        <a href="https://www.dropbox.com/s/34vy4o5fthhz77d/coseg.tar.gz" target="new">COSEG segmentation dataset</a><br>
        <a href="https://www.dropbox.com/s/s3n05sw0zg27fz3/human_seg.tar.gz" target="new">Human Segmentation dataset</a><br>
        <a href="https://www.dropbox.com/s/2bxs5f9g60wa0wr/cubes.tar.gz" target="new">Cubes classification dataset</a><br>
        <a href="https://www.dropbox.com/s/w16st84r6wc57u7/shrec_16.tar.gz" target="new">Shrec classification dataset</a><br>
        See our github page for how to run our code on these datasets.
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    <h2>Contact</h2>
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        Rana at Hanocka dot com
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